Based on the number of minutes that Felix takes to exercise and the minutes he takes to warm up, the equation given does not describe the statement.
How to describe the statement as an equation?The number of minutes that Felix spends exercising and the number of minutes he spends running, should be added together to find the number of minutes Felix spends exercising in one session.
This means that the total minutes for exercising is:
= 12 + 20
= 32 minutes per session
The number of sessions that Felix exercised to get to a total of 240 minutes is therefore:
Number of minutes per session x Number of sessions = 240 minutes
Assuming the number of sessions is x, the equation would be:
32 × x = 240
32x = 240
The given equation of 20 + 12x=240 is therefore not described by the statement.
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A home has a triangular backyard. The second angel of the triangle is 3 more than the first angel. The third angel is 9 more than four times the first angel.
The measure of three angles of triangular backyard are 28°, 31° and 121°.
Given that, a home has a triangular backyard.
What is the angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Let the measure of first angle be x.
The second angel of the triangle is 3 more than the first angel = x+3
The third angel is 9 more than four times the first angel = 4x+9
Using angle sum property of a triangle
x+x+3+4x+9 = 180°
⇒ 6x + 12 = 180
⇒ 6x = 168
⇒ x = 28°
So, x+3 = 31° and 4x+9 = 121°
Therefore, the measure of three angles of triangular backyard are 28°, 31° and 121°.
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eleven is fifteen more than four times a number.
translate to an equation. let x be the unknown number . solve for x
The equation is 15+4x= 11 and the value for x= -1
what are equations?An equation is a mathematical statement between two expressions that have equal values. For example, 15+4x= 11. The symbol = shows that 11 and 15+4x are the same
Word problems can be translated into equation with variables.
Representing the unknown with x,
4×x= 4x
the word problem is therefore translated to
11= 15+4x
collecting like terms
4x= 11-15
4x= -4
divide both side by 4
x=-1
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Select the statement that correctly compares two numbers. (2 points)
Group of answer choices
4.09 = 4.90
2.03 < 2.021
1.470 > 1.70
0.36 > 0.187
Answer:
the last one
Step-by-step explanation:
you have to look at which number is bigger than the other
it usually depends which number is first
ex:
3>1
0.3>0.1
0.3>0.12
If e-X = 6. write x in terms of the natural logarithm. O In 6 In -6 O -In 6 06
to cancel the exponential we apply natural log on both sides
[tex]\begin{gathered} \ln (e^{-x})=\ln 6 \\ -x=\ln 6 \end{gathered}[/tex]multiply -1 on each side
[tex]x=-\ln 6[/tex]Find the intersection points when the line y = 12-4x meets the curve y =12-x^3. Hence, sketch in the same diagram, the line y = 12 - 4x and the curve y=12-x^3 Calculate the area of the region bounded by the curve and the line
The equations of the line and the curve are
[tex]\begin{gathered} y=12-4x \\ y=12-x^3 \end{gathered}[/tex]We will equate their right sides to find the values of x
[tex]12-4x=12-x^3[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 12-12-4x=12-12-x^3 \\ -4x=-x^3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-4x}{-1}=\frac{-x^3}{-1} \\ 4x=x^3 \end{gathered}[/tex]Subtract 4x from both sides
[tex]\begin{gathered} 4x-4x=x^3-4x \\ 0=x^3-4x \end{gathered}[/tex]Switch the two sides
[tex]x^3-4x=0[/tex]Take x as a common factor
[tex]\begin{gathered} x(\frac{x^3}{x}-\frac{4x}{x})=0 \\ x(x^2-4)=0 \end{gathered}[/tex]Factor the bracket using the rule of the difference between two squares
[tex](a^2-b^2)=(a+b)(a-b)[/tex][tex]\begin{gathered} (x^2-4)=(x+2)(x-2) \\ x(x+2)(x-2)=0 \end{gathered}[/tex]Now, equate each factor by 0
[tex]\begin{gathered} x=0 \\ x+2=0,x-2=0 \\ x=-2,x=2 \end{gathered}[/tex]Substitute the values of x in the equation of the line to find their corresponding values of y
[tex]\begin{gathered} y=12-4(0)=12 \\ y=12-4(-2)=12+8=20 \\ y=12-4(2)=12-8=4 \end{gathered}[/tex]The points of intersection between the line and the curve are
(0, 12), (-2, 20), (2, 4)
Let us draw the graph
The red line represents the equation of the line
The blue curve represents the equation of the curve
To find the area bounded between the line and the curve we will use the integration
Since the line is above the curve at the point (-2, 20), then
We will subtract the curve from the line and use the values of x -2 and 2 as the limits of integration
[tex]A=\int_{-2}^2[(12-4x)-(12-x^3)]dx[/tex]Simplify the terms inside the brackets first.
[tex]\begin{gathered} A=\int_{-2}^2[12-4x+12+x^3]dx \\ A=\int_{-2}^2[-4x+x^3]dx \end{gathered}[/tex]In integration, we will add the power by 1 and divide the term by the new power
[tex]A=[\frac{-4x^{1+1}}{1+1}+\frac{x^{3+1}}{3+1}]_{-2}^2[/tex]Simplify it
[tex]\begin{gathered} A=[\frac{-4x^2}{2}+\frac{x^4}{4}]_{-2}^2 \\ A=[-2x^2+\frac{x^4}{4}]_{-2}^2 \end{gathered}[/tex]Substitute x by 2 and -2, then subtract the answer
[tex]A=[-2(2)^2+\frac{2^4}{4}]-[-2(-2)^2+\frac{(-2)^4}{4}][/tex]Solve each bracket
[tex]A=8[/tex]The area of the region bounded between the line and the curve is 8 square unit
What is the answer to 4.18 + 86.53=
Answer:
90.71
Step-by-step explanation:
Just columnar addition
What kind of compound inequality is 1-4x<21 and 5x+2>22?
The compound inequality is 5x + 2 > 22 large i.e., x > 4.
Given,
1 - 4x < 21 and 5x + 2 >22
What is Compound Inequality?
A compound inequality is an inequality that merges two inequalities either by using "and" or "or". Sometimes "and" won't be specifically mentioned but it is understood. For example, 1 < x < 3 is nothing but "x > 1 and x < 3".
To solve the above Inequality:
1 - 4x < 21 and 5x + 2 >22
Now,
1 - 4x < 21
=> 1 - 21 < 4x
=> -20 < 4x
=> x > -5
5x + 2 > 22
=>5x > 20
x > 4
Hence, The compound inequality is 5x + 2 > 22 large i.e., x > 4.
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The circle below is centered at (10,4) and has a radius of 4. What is itsequation?101010O A. (x - 10)2 + (y - 4)2 = 16O B. (x-4)2 + (-10)2 = 4O C. (x-4)2 + (-10)2 = 16OD. (x-10)2 + (x-4)2 = 4
The general equation of a circle with centre (h,k) and radius r is given as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where,} \\ (h,k)=(10,4) \\ r=4 \end{gathered}[/tex]By substitution, we will have,
[tex]\begin{gathered} (x-10)^2+(y-4)^2=4^2 \\ =(x-10)^2+(y-4)^2=16 \end{gathered}[/tex]Hence,
The correct answer is OPTION A
Due to temporary tax cuts in 2010, a person with typical deductions earning $50,000 per year would have saved 2% of their income plus $850 in federal taxes. How much money did a typical person save?
If the person earns $50,000, we must find how much is 2% of that and then add it to $850. Then we would have how much a typical person saves.
First let's find 2% of $50,000
[tex]\begin{gathered} 2\%\text{ of }50000=\frac{2}{100}\cdot500000=\frac{2\cdot50000}{100}=\frac{100000}{100}=1000 \\ \\ \\ \end{gathered}[/tex]Therefore 2% of $50,000 is $1000. Now we add it to $850 and we get
[tex]1000+850=1850[/tex]The final result is $1850
Solve the inequality.
-1/4 y > -6
Answer:
y < 24
Step-by-step explanation:
The inequality of -1/4 y > -6 is y< 24
Let's solve your inequality step-by-step.
[tex]\frac{-1}{4} > -6[/tex]
Step 1: Multiply both sides by [tex](\frac{4}{-1} )[/tex]
[tex]=(\frac{-1}{4}) (\frac{4}{-1} ), -6 (\frac{4}{-1} )\\= y < 24\\[/tex]
Answer y< 24
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Why is unit rate the only attribute we use to compare proportional relationships? Consider the graph of a
proportional relationship and the attribute(s) that all proportional relationships share to help you answer this
question.
Answer:
Step-by-step explanation:
Because its an internationally accepted method.
Drag each tile to the correct box. Not all tiles will be used.
Match each function to the correct scenario.
f(x) = 10(1.025)*
f(x) = 7(1.50)*
f(x) = 50(1.07)*
f(x) = 25(1.10)*
f(x) = 15(0.25)*
f(x) = 15(1.25)*
The price of a movie ticket is currently $10 but increases at a rate of 2.5% per
year.
There are currently 15 students with laptops, and the number increases at a
rate of 25% per year.
An animal shelter has 50 dogs, and the number of dogs increases by 7% per
year.
Submit
000
The correct matching of the functions is as follows:
(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per year: (1) f(x) = 10(1.025)(B) There are currently 15 students with laptops, and the number increases at a rate of 25% per year: (6) f(x) = 15(1.25)(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per year: (3) f(x) = 50(1.07)What are functions?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. Four broad categories can be used to classify different types of functions. One-to-one function, many-to-one function, onto function, one-to-one, and into function—all based on the element.So, matching each function with a correct scenario:
(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per year: (1) f(x) = 10(1.025)(B) There are currently 15 students with laptops, and the number increases at a rate of 25% per year: (6) f(x) = 15(1.25)(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per year: (3) f(x) = 50(1.07)Therefore, the correct matching of the functions is as follows:
(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per year: (1) f(x) = 10(1.025)(B) There are currently 15 students with laptops, and the number increases at a rate of 25% per year: (6) f(x) = 15(1.25)(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per year: (3) f(x) = 50(1.07)Know more about functions here:
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The correct question is given below:
Drag each tile to the correct box. Not all tiles will be used.
Match each function to the correct scenario.
f(x) = 10(1.025)*f(x) = 7(1.50)*f(x) = 50(1.07)*f(x) = 25(1.10)*f(x) = 15(0.25)*f(x) = 15(1.25)*(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per
year.
(B) There are currently 15 students with laptops, and the number increases at a
rate of 25% per year.
(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per
year.
Submit
000
Mumbai is approximately
845
845845 kilometers
(
km
)
(km)left parenthesis, start text, k, m, end text, right parenthesis away from Bangalore, and Mumbai is approximately
1160
km
1160km1160, start text, k, m, end text away from Delhi. The distances, measured in centimeters
(
cm
)
(cm)left parenthesis, start text, c, m, end text, right parenthesis, between the cities on Allyson's map are proportional to the real distances
Answer:
A the answer is a
Step-by-step explanation:
btc u lied jj
Answer:
B, D, and E
Step-by-step explanation:
to whoever said btc u lied-
is also wrong : )
Find all Polar coordinates of point P where P= (5,-π/6)
Given :
[tex]P\text{ = (5, }\frac{-\pi}{6})[/tex]Required: All polar coordinates of the given point
We can have the following points:
[tex]\begin{gathered} (5\text{ , }\frac{-\pi}{6}\text{ + 2n}\pi)\text{ or (-5 ,( }\pi-\frac{-\pi}{6}+\text{ 2n}\pi)\text{ )} \\ \text{This simplifies to } \\ (5\text{ , }\frac{-\pi}{6}\text{ + 2n}\pi)\text{ or (-5, (}\frac{-\pi}{6}\text{ + (2n + 1)}\pi) \end{gathered}[/tex]The correct option is the third option
On a coordinate plane, each point on ST is defined by coordinates (x,y). The segmentis rotated 90° counterclockwise to create S'T'. Which of the following defines a pointon S'T' that corresponds to a point on ST.
The coordinates of S'T' are (-y,x)
Here, we want to get the result of rotating a point 90 degrees counterclockwisely
What we have here is that we will have a change in the coordinates of the point as follows;
[tex](x,y)\Rightarrow\text{ (-y,x)}[/tex]One of your classmates was absent on the day that you learned how to write and solve an equation from a contextual situation. Your teacher has asked you to explain the four steps and their application to the problem that follows.
Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, how many did Elena steal?
Using the four steps from this lesson, write and solve an equation to find the number of bases Elena stole.
The number of bases Elena stole is 9 if Natasha stole three fewer bases than twice the number Elena stole.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases,
Let n be the number of bases stolen by Natasha
Let e be the number of bases stolen by Elena.
From the data given in the question:
The linear equation in two variables can be framed:
n = 2e -3
Plug n = 15
15 = 2e - 3
After solving:
e = 9
e = 9 bases stolen by Elena
Thus, the number of bases Elena stole is 9 if Natasha stole three fewer bases than twice the number Elena stole.
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The perimeter of a rectangle is 260 feet find the length and width if the length is an even integer in the width is 5 times the next consecutive even integers
The rectangle is 20 feet long and 50 feet wide.
Let the length be x. So, the next consecutive integer will be (x + 2). Width of rectangle = 5(x + 2). As per the formula, perimeter of rectangle is 2(length + breadth).
Keep the values in formula to find the value of x.
2(x + 5(x + 2)) = 260
Firstly solving the inner bracket
2(x + 5x + 10) = 260
Now again opening the bracket
2x + 10x + 20 = 260
Performing addition
12x = 260 - 20
Performing subtraction
12x = 240
x = 240 ÷ 12
Performing division
x = 20
Length of rectangle = 20 feet
Width of rectangle = 2(20 + 5)
Width of rectangle = 2×25
Width of rectangle = 50 feet
So, the length and width of rectangle is 20 feet and 50 feet.
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I want help answering part c on question 5 to figure out what the measure of angle ROS is
We are given a system of acute angles and are asked to intuitively resolve the different unknown angles while we know some.
Our approach is to create a system of equations that will help us easily separate the different angles as much as possible.
[tex]undefined[/tex]A car can travel 20 4/5 miles on 4/5 gallons of gas. What is the unit rate for miles per gallon
Answer:
26 miles per gallon
Step-by-step explanation:
[tex] \frac{20.8}{.8} = \frac{208}{8} = 26[/tex]
a right triangle ABC is shown below the area of the triangle above will equal 1/2 of the rectangle that is 5 units long and underscore units wide
for the ahe area of triangle
Height of the triangle = 2 units, base= 5 unit
Area of triangle =1/2 Breadth x height
Susbtitute the value and simplify:
[tex]\begin{gathered} \text{ area of triangle=}\frac{1}{2}\times2\times5 \\ \text{ area of triangle= }5\text{ units} \end{gathered}[/tex]Answer =5 units
Find the hypotenuse where relevant, give your answers to 3 significant figures.
The Pythagorean Theorem states that for Right Triangles:
[tex]c^2=a^2+b^2[/tex]Where "c" is the hypotenuse (the longest side of the triangle), and "a" and "b" are the legs of the Right Triangle.
In this case, you can see that the exercise provides the length of the legs of the Righ Triangle, but you don't know the hypotenuse. Then, you can set up that:
[tex]\begin{gathered} a=6\operatorname{cm} \\ b=8\operatorname{cm} \end{gathered}[/tex]Therefore, you can substitute values into the equation that represents the Pythagorean Theorem and solve for the hypotenuse:
[tex]\begin{gathered} c^2=(6\operatorname{cm})^2+(8\operatorname{cm})^2 \\ c=\sqrt[]{(6\operatorname{cm})^2+(8\operatorname{cm})^2} \\ \\ c=\sqrt[]{100\operatorname{cm}^2} \\ c=10\operatorname{cm} \end{gathered}[/tex]Hence, the answer is:
[tex]c=10\operatorname{cm}[/tex]The ceiling of Judy's living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Judy can buy rolls that each contain 20 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.
Given the following question:
Judy's room is a square 15 feet long on each side
One roll of crepe paper equals 20 feet
[tex]\begin{gathered} \text{perimeter =} \\ 4\times s \end{gathered}[/tex][tex]\begin{gathered} 4\times15=60 \\ p=60ft \end{gathered}[/tex]The line she plans to hang the crepe paper from one corner to it's oppsite corner. So think about a X in the middle of the square. Since it's a square it will be particually smaller than the actual length of each side of the square.
[tex]60\div10=6[/tex]Let 10 represent the length of one side of the X
Let 60 represent the perimeter
Judy will need a minimum of 6 rolls of crepe paper for this party.
What is the variable terms in 4x-2y+3
The variables of the expression 4x-2y+3 are x and y
What is Variables?
Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Variables include things like age, sex, business revenue and expenses, country of birth, capital expenditures, class grades, eye color, and type of vehicle.
Given expression,
4x-2y+3
Variable is a representation of an unknown numerical value in an equation or algebraic statement by a symbol, typically a letter.
In this expression
4x - 2y + 3
The variable in this expression is x and y
Hence, the variables are x and y
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the blank of a fraction is the part that tells how many units the fraction contains
Answer:
The Denominator of a fraction is the part that tells how many units the fraction contains.
(Got it from another Expert-Verified answer)
Answer:
Step-by-step explanation:
numerator
(x-8)(2x+5)=0 solve the equation
Solution:
Given the equation:
[tex](x-8)(2x+5)=0[/tex]To solve the equation, we use the zero factor principle.
From the zero factor principle, we have
[tex]\begin{gathered} When\text{ } \\ ab=0 \\ \Rightarrow a=0\text{ or b=0} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} x-8=0\text{ or 2x+5 =0} \\ when \\ x-8=0 \\ add\text{ 8 to both sides of the equation} \\ x-8+8=0+8 \\ \Rightarrow x=8 \\ when \\ 2x+5=0 \\ add\text{ -5 to both sides of the equation,} \\ 2x+5-5=0-5 \\ \Rightarrow2x=-5 \\ divide\text{ both sides by the coeffient of x, which is 2} \\ \frac{2x}{2}=\frac{-5}{2} \\ \Rightarrow x=-\frac{5}{2} \end{gathered}[/tex]Hence, the solution to the equation is
[tex]x=8,\text{ x=-}\frac{5}{2}[/tex]Use the following image to answer the question.CBFGHHow would you identify IE?
Given:
Center of circle = Point O.
Let's use the image to identify line IE.
Since E is the center of the circle and point I is on the circumference of the circle, line IE starts from the point I and goes to the center of the circle, point E.
Hence, we can say line IE is the radius of the circle.
The radius of a circle can be said to be the distance from the center of a circle to any point on the circumference of the circle.
Therefore, IE is the radius of the circle.
• ANSWER:
Radius
A medical survey was conducted in order to establish the proportion of the population which was infected with cancer. The results indicated that 40% of the population was suffering from the disease. A sample of 6 people was later taken and examined for the disease. Find the probability that the following outcomes were observed:
Only one person had the disease (4 mks)
Exactly two people had the disease (4 mks)
At most two people had the disease (4 mks)
At least two people had the disease (4 mks)
Three or four people had the disease (4 mks)
The probability that Only one person had the disease is 0.1866, Exactly two people had the disease is 0.311, At most two people had the disease is 0.0467, At least two people had the disease is 0.9533, Three or four people had the disease is 0.41472 for the given distribution.
What is Probability?
The probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.Given that,
n=6
P=40%=0.4
q=0.6
(i) P(X=1)=6C1(0.4)^1(0.6)^(6-1)
= 6X0.4X(0.6)^5
=0.1866
(ii) P(X=2)=6C2(0.4)^2(0.6)^(6-2)
=15X(0.4)^2X(0.6)^4
=0.311
(iii) P(X≥2)=1-P(X<2)
=1-[P(X=0)+P(X=1)+P(X=2]
P(X=0)=6C0(0.4)^0(0.6)^6-0
=0.0467
(iv) P(X≤2)= 1- P(X≥2)
=1-0.0467
=0.9533
(v)P(X=3)+P(X=4)=6C3(0.4)^3(0.6)^(6-3)+6C4(0.4)^4(0.6)^(6-4)
=6C3(0.4)^3(0.6)^(6-3)+6C4(0.4)^4(0.6)^(6-4)
=20X0.013824+15X0.009216
=0.41472
The probability that Only one person had the disease is 0.1866, Exactly two people had the disease is 0.311, At most two people had the disease is 0.0467, At least two people had the disease is 0.9533, Three or four people had the disease is 0.41472 for the given distribution.
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The graph of a function is shown below . What is true about the function between x=1 and x=5
The true statement about the function between x = 1 and x = 5 is that the function decreases at this interval
How to interpret the graph?The graph of a function represents the given parameter
Also, we have the interval to be
x = 1 and x = 5
From the function, we can see that
f(5) < f(1)
This means that:
The function values decrease from x = 1 to x = 5
The general conclusion of this is that this interval represents a decrement in the values of the function
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Im stuck on question 5-91 in cpm geometry the question asks me to find the area of a triangle... I figured out the 30 60 90's are but i still have triangle left over ill send a photo of the triangle
Answer
Area of the triangle = 72 square units
Explanation
For a triangle whose two sides (a and b) are given, and an angle that exists between them is also given, the area of that triangle is given as
Area of the triangle = ½ ab Sin θ
For this question,
a = 12 units
b = 24 units
θ = 30°
Area of the triangle = ½ ab Sin θ
Area of the triangle = ½ (12) (24) (Sin 30°)
Sin 30° = 0.5
Area of the triangle = ½ (12) (24) (Sin 30°)
Area of the triangle = ½ (12) (24) (0.5) = 72 square units
Hope this Helps!!!
Luke ate a snack with 91 calories If the chips he ate were 41.2 calories were in the rest of his snack?
We have
91 calories in total
he ate 41.2 calories
we need to subtract
91 calories - 41.2 calories= 49.8
There are 49.9 calories in the rest of this snack
