You should spend 30 minutes on machine 1 and 10 minutes on machine 2.
Given,
In the question:
You have 40 minute to exercise at the gym, and you want to burn a total of 300 hundred calorie using both machine.
Now, According to the question;
300 calories in 40 minutes can be set up as a ratio to find out how many calories per hour or calories per minute you are trying for:
300 calories /40 minutes = x calories/60 minutes for calories per hour (you are aiming for 450 calories burned per hour)
300 calories / 40 minutes = 7.5 calories per minute if you want to look at it that way instead.
One version of this problem that I found online completes the setup this way:
First machine is 8 calories per minuteSecond machine is 6 calories per minuteThis allows us to set up a system of equations. The first equation will be for calories burned:
8x + 6y = 300
x is minutes on the 8 calorie per minute machine; y is minutes on the 6 calories per minute machine.
A second equation simply shows that the total minutes add up to 40:
x + y = 40
Now you can use substitution, elimination, or linear combinations to solve the system. I'll use substitution to rewrite the second equation:
x = 40 - y....(1)
Now substituting into the first equation:
8(40 - y) + 6y = 300
320 - 8y + 6y = 300
2y = 20
y = 10
Put the value of y in eq.(1)
Then, x gives the 30
Hence, You should spend 30 minutes on machine 1 and 10 minutes on machine 2.
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3. For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation
for the cost, C, after h hours of babysitting. What do you think the slope and the y-
intercept represent? How much money will she make if she baby-sits 5 hours? Graph
Given various values of the linear functions f (x) and g(x in the table, determine the y-intercept of (f − g)(x).
x −6 −4 −1 3 4
f (x) 20 14 5 −7 −10
g(x) −36 −26 −11 9 14
(0, 4)
(0, −4)
(0, 8)
(0, −8)
The y-intercept of (f − g)(x) is 8. Therefore, option C is the correct answer.
Given various values of the linear functions f (x) and g(x) in the table.
What is a y-intercept?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
For the function f(x)
Here, (-6, 20) and (-4, 14)
Slope =(14-20)/(-4+6)
= -3
Substitute, m=-3 and (x, y)=(-6, 20) in y=mx+c, we get
20=-3(-6)+c
c=2
Substitute, m=-3 and c=2 in y=mx+c, we get
f(x)=-3x+2 --------(I)
For the function g(x)
Here, (-6, -36) and (-4, -26)
Slope =(-26+36)/(-4+6)
= 10/2 =5
Substitute, m=5 and (x, y)=(-6, -36) in y=mx+c, we get
-36=5(-6)+c
c=-6
Substitute, m=5 and c=-6 in y=mx+c, we get
g(x)=5x-6 --------(II)
Now, (f − g)(x)=-3x+2-(5x-6)
= -3x+2-5x+6
= -8x+8
Here, y-intercept is 8
The y-intercept of (f − g)(x) is 8. Therefore, option C is the correct answer.
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A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 164 pounds requires 205
milligrams of medicine. What is the weight of a patient who requires 173.75 milligrams of medicine?
pounds
The amount of medicine required for a patient whose weight is 173.75 pounds will be equal to 217.18 milligrams.
What is the ratio?The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities to compare them.
As per the data given in the question,
Weight of patient = 164 pounds
Medicine for 164 pounds weight = 205 milligrams
Weight of another patient = 173.75 pounds
Let the amount of medicine required is x.
So,
164 pounds = 205 milligrams and,
173.75 pounds = x milligrams
Perform Cross-multiplication,
164x = 205 × 173.75
x = 35618.75/164
x = 217.18 milligrams.
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Pls help will make brain crown thing
Answer:
10,5 should be changed
Step-by-step explanation:
hope this helps
ther are a total of 60 gils and boys in a math class there are 4 times as many boys as girls in the class how many grls and boys are in the class
The number of boys in the class = 48 boys
The number of girls in the class = 12 girls
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of boys in the class be = x
Let the number of girls in the class be = y
Now , the total number of students in the class = 60
So , the equation , will be
x + y = 60 be equation (1)
Now , the number of boys = 4 times the number of girls
So , the equation will be
x = 4y be equation (2)
Substitute the value of equation (2) in equation (1) , we get
4y + y = 60
On simplifying the equation , we get
5y = 60
Divide by 5 on both sides of the equation , we get
y = 12
So , the value of y is 12
Substitute , the value of y in equation (2) , we get
x = 4y
x = 4 x 12
x = 48
Therefore , the number of boys is 48 and the number of girls is 12
Hence , The number of boys in the class = 48 boys
The number of girls in the class = 12 girls
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Rex deposited $900 into an
account that earns 4% simple
interest. How many years will it
take for the value of the
account to reach $1,800?
The number of years for the value of $900 to reach $1,800 if the rate of interest is 4%, is 25 years.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The amount after some years, A = $1800,
The rate of interest, r = 4% per annum,
The principal amount, p = $900,
Calculate the number of years as shown below,
A = P + SI
1800 = 900 + p × r × t / 100
Here, t is the time in years,
1800 - 900 = 900 × 4 × t / 100
900 = 3600t / 100
900 = 36t
t = 900 / 36
t = 25
Thus, the number of years will be 25.
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Use the original price and the markdown to find the retail price.
Original price: $110; Markdown: 30%
Answer:
Step-by-step explanation:
regergergr
In slope intercept form, write the equation for each line.
Answer:
A: y = -0.4x -5
B: y = -1x +7
C: y = 1.25x +7
D: y = 3x -5
Step-by-step explanation:
See the attached worksheet. Finding the equations for the graph lines is reasonabvly straightforward, but the number of lines quadruples the space required. We'll find equations of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0). The worksheet notes the 4 steps needed:
1. mark any two points on the graph for each line.
2. Find the slope for each line by calculating the Rise/Run
3. Find the y-intercepts from the graph.
4. Assemoble the slopes and intercepts into the four equations.
Use a spreasheet to keep organized, and nbe patient. Check the equations using a free online graphing utility (e.g., DESMOS).
Jovan is tired of measuring all the angles and sides to determine
if two triangles are similar. "There must be an easier way," he
thinks. "What if I know that all of the angles are congruent?
Does that mean that the triangles are similar?"
Answer:
yes congruent means identical of the same
Step-by-step explanation:
hope this helps
Answer: The answer is here
Step-by-step explanation:
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.
If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.
a. Using parallel line relationships, find the value of
x. Use the relationship between the two marked
angles to set up your equation.
Show your work to support your answer. (4 pts)
x =
b. Find the measure of each of the angles. Don’t forget to label your answers.
Answer:
a and f are 14°
Angles b, c, d, and e are all 166°
Step-by-step explanation:
Alternate interior angles are congruent
x + 9 = 4x - 6 Subtract x from both sides
9 = 3x - 6 Add 6 to both sides
15 = 3x Divide both sides by 3
5 = x
Plug this back into the equation for find the angles measurements
x + 9
5 + 9
14
or
4x _ 6
4(5) -6
20 - 6
14
angles a and f are vertical angles so they are congruent and equal to 14
B ,c , d and e are all supplements to the found angles
180-14 = 166
What is the answer I need answers now I'm going to fail pls explain to I need answers quickly.
The factorization given is not a prime factorization.
Given that,
A factorization of a number is given we have to discuss whether the factors are prime factors or not.
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
here,
Given factorization = 2² + 3 + 5⁴ + 8 + 11².
Since the above 8 cannot be taken in prime factor,
So the given factorization is not the prime factorization of the number.
Thus, the factorization given is not a prime factorization.
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find the value of the unknowns
chapter matrices. with full explanations and working.
The unknowns in the given matrix total must have the values w = -5, z = 15, and y = 1.
Given,
To determine the value of the unknowns in the matrix,
What is the matrix?A matrix is a rectangular array made up of numbers that are arranged in rows and columns. The figures are known as matrix elements or entries. Matrices are widely utilized in engineering, physics, economics, and statistics, as well as many other.
Here,
From the above matrix,
Equation formed,
2z -18 = 12
z = 15
2w + 6 = 16,
w = 5,
10 - 6 = 4y
y = 1
Thus, The unknowns in the given matrix total must have the values w = -5, z = 15, and y = 1.
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You move left 7 units. You end at (-3, -5). Where did you start?
Answer:
[tex](4 , -5)[/tex]
Step-by-step explanation:
Note that when you move left or right any amount of units, you will be making the changes to the x-variable. If you move up or down any amount of units, you will be making the changes to the y-variable.
In this case, it is given that:
(x , y) = (-3 , -5)
You will want to move right 7 units, as you are trying to find your starting position. Add 7 from the x variable:
[tex](x , y) = (-3 , -5) = (-3 (+7) , -5)\\\\= (-3 (+7) , -5)\\= ((-3 +7) , -5)\\= (4 , -5)[/tex]
[tex](4 , -5)[/tex] is your starting position.
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after 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) what is the half-life of radon-222? (b) how long will it take the sample to deca
The half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.
What is half life of an element?The half-life of a radioactive is time for 50% of its particles to decay or disintegrate into a new element. The pace at which a radioactive material will decay is predicted using this indicator of an isotope's stability. An element's half-life, which differs substantially across various elements, is based on the unique characteristics of its nucleus.
For instance, the half-life of uranium-238 is 4.5 billion years whereas that of carbon-14 is 5,730 years. This indicates that half of the carbon-14 atoms in a sample will have decayed after 5,730 years, and half of the uranium-238 atoms will have decayed after 4.5 billion years.
How to solve?
(a) After 3 days, the sample has decayed to 58% of its original amount, which means that half of the original amount has already decayed. Therefore, the half-life of radon-222 is 3 days.
(b) Since the half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.
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X to the power of 3 - 5X
Answer:
it's so simple like very simple
Step-by-step explanation:
you just have to do
5x-3=2
x=2
X | 0 | 1 2 3
y|-2| 0 [?][ ]
Answer: 2, 4
Step-by-step explanation:
Assuming this is a linear relationship, [tex]y[/tex] increases by 2 whenever [tex]x[/tex] increases by 1.
So, the blanks in the table are [tex]0+2=2[/tex] and [tex]2+2=4[/tex], respectively.
what is the circumference of a circle with a diameter of 58 inches
Answer:
58π or about 182.12
Step-by-step explanation:
In order to find circumference with diameter, you need to use the formula:
C = πd
Multiply the diameter (58) by pi, and since pi is an irrational number, let's use 3.14.
3.14(58) = 182.12
58π would be the answer as well if you don't multiply pi.
Compare the function f(x)=3x-1/2 to the function shown in the graph. Which statements are
correct?
Please help! Fin, the measures of the numbered angLes 1 and 4!
Applying the properties of a rhombus, the measures of the numbered angles are:
m<1 = 58°
m<2 = 90°
m<3 = 32°
m<4 = 58°
What are the Properties of a Rhombus?Some properties of a rhombus include:
Angles that are opposite each other are congruent/equal.Diagonals intersect each other at right angles.Diagonals bisect each angle in a rhombus.Adjacent angles are supplementary.Given the rhombus in the image above, the numbered angles are:
m<3 = 32° [opposite angles are equal]
m<2 = right angle = 90°
m<1 = 180 - 90 - 32 = 58°
m<1 = m<4
m<4 = 58°
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Solve each system by elimination: 3x-7y=6 2x+7y=4
Answer:
Your answer is [tex]x=2[/tex] and [tex]y = 0[/tex]
Step-by-step explanation:
(attached)
Answer:
(2,0)
x=2, y=0
Step-by-step explanation:
(-2)3x-7y=6(-2)
(3)2x+7y=4(3)
-6x+14y=-12
6x+21y=12
-6x+14y=-12+6x+21y=12
35y=0
y=0
sub into one of the original equations
2x+7(0)=4
2x=4
x=2
The denominator of a fraction is 2 more than the numerator. If 1 is added to both, the fraction reduces to 4/5. Find the fraction
The fraction is 7/9 according to given information.
What is fraction?
A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken of in everyday English. A common, vulgar, as well as simple fraction is one that has a non-zero denominator displayed below (or after) the line that separates the numerator from the denominator. Compound fractions, complex fractions, as well as mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.
Main Body:
Let the fraction be a/b
In First condition
b = a + 2(1)
In Second condition
a + 1/b + 1 = 4/5
5(a + 1) = 4(b + 1)
5a + 5 = 4b + 4
5a - 4b = 4 - 5
5a - 4b = -1
Using 1
5a - 4(a + 2) = -1
5a - 4a - 8 = -1
a = 8 - 1
a = 7
Now,
Using 1
b = a + 2
b = 7 + 2
b = 9
Fraction = a/b = 7/9
hence , the fraction is 7/9.
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A tennis ball is dropped from a certain height. Its height in feet is given by
h=-16t²+36 where t represents the time in seconds after launch. How long is
the ball in the air?
The amount of time the tennis ball will be in the air after launch is √2 seconds.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
The height of the tennis ball is given by the function h = - 16t² + 36, where t represents time in seconds.
Now, The amount of time the tennis ball will be in the air can be determined by the time when it hits the ground and at that time height of the ball should be zero.
Therefore, The time in the air is,
0 = - 16t² + 36.
16t² = 36.
t² = 2.
t = + √2 seconds, as time can not be negative.
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Shaun won 6 out of the 10 video games he played. What percent of the video games did Shaun win?
Answer:
60%
Step-by-step explanation:
Shaun won 60% percent of the games.
Answer:
Shaun won 60% out of the 10 video games he played.
Step-by-step explanation:
If Shaun played 10 video games and only won six out of all of them, he won 60% since we can count 10 as 100% and 6 as 60%.
GEOMETRY HELP NEEDED
Answer:
this is easy get a protractor
Step-by-step explanation:
Find the slope of the line write your answer in simplest form -4,1 1,-2
Find the measure of angle f given the information below.
Answer:
53 degrees
Step-by-step explanation:
This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees) - a. Then, because g + f + e = 180 (since it is a straight line), substitute the values that we know and solve. (61) + f +(66) = 180. f = 53
A blueberry pie is made of 10 inch diameter pie pan.the pie is cut into 8 equal slides.what is the area of 1 slice
Cutting perfect slices of pie can be tricky. Crusts can crumble, bottoms can buckle and fillings can spill over, but there are a lot of tricks for a good slice.
What is diameter?In a circle, diameter is a line that passes through the center and meets the circumference at opposite ends. It is twice as long as that of the radius of the circle. In other words, the diameter of a circle is the line that passes through the center and divides the circle into two equal parts. Let us learn more about diameter definition and properties in this article.The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circumference of the circle. The diameter is also known as the longest chord of the circle.To learn more about diameter refer to:
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6th Grade Math Inequalitys
U
44°
T
V
R
25°
S
mTQ= type your answer...
type your answer.
mTQ=
mQR =
mTS =
mSQR
mRQT =
=
mTS=
mQR=
Answer:
Step-by-step explanation:
TQ = 44 + 25 = 69°
QR = 180 - 25 = 155°
TS = 180 -(44 + 25) = 180 - 69 = 111°
SQR = 180 + 155 = 335°
RQT = 180 + 44 = 224°
What is the value of x?
Use picture below:
please help, I'm literally bEgGiNg-
The value of x is 135°
What is Exterior Angle Theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.
An exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.
Linear pair of angles are,
∠1 + ∠2 = 180°
where, ∠1 is exterior angle
and, ∠2 is interior angle
Given ,
One angle is = 90°
Then other two angle will be = 45° and 45°
Now, According to Exterior angle property,
x + 45 = 180
x = 180 - 45
x = 135°
Hence, the value of x is 135°
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